We can always make polymers and HydroCarbons in general from other sources if we have energy abundance. We literally can just capture the CO2 we emitted from burning fossil and make it plastics.
Of course this does not make sense in a world where we do not have enough energy to even keep datacenters open.
Edit: To clarify, I do not propose burning fossils to capture CO2 and make plastics. I am a Thermo Laws believer.
The problem with carbon capture from air is the low carbon concentration. Try to do the math for how much air you need to process to get even one barrel of oil worth of hydrocarbons from a DAC process.
That sounds like a hack from late-game Factorio: pollute enough that you can just pull iron filings right out of the air. Everyone wins! Except the meatbags who need to breathe the air …
Methane >> carbon dioxide as a polyethylene/linear polymers feed stock. Double bonded oxygens are hella higher affinity than four loose hydrogens. Also as pointed out, even in a concentrated combustion effluent stack CO2 is low concentration at atmospheric pressure.
I don’t know about methane as an aromatic/hybridized ring building block. Anything is possible with chemical synthesis but is it energy feasible.
There’s always plant hydrocarbon feed stocks but I think using arable land to make plastics is dumb and also carbon intensive. (I do wear cotton clothing tho because you need to make trade offs).